Made available in DSpace on 2018-06-27T19:12:57Z (GMT). No. of bitstreams: 2 Rosi Meri Dornelles Brandao Costa.pdf: 29981045 bytes, checksum: a2373aff499cc9e78fe4be61d82ea511 (MD5) Rosi Meri Dornelles Brandao Costa.pdf.jpg: 3591 bytes, checksum: 719ad7f8b8035f4c8d8a5e8c34ef681c (MD5) Previous issue date: 2012-06-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This research it aimed to determine the contributions of class construction, in interaction with the use of media resources to enhance skills development and minimize gaps in mathematical knowledge in the final years of elementary school. In an attempt to overcome these shortcomings, the study occurred in two distinct stages of implementation of proposed activities: the first was the lesson and the teaching process, supporting and preparing for the second time, which included interactive activities through Treasure Hunt using the computer as a technological resource and its interfaces to better qualify collaborative learning. The study was conducted with students in the 6th grade of a public elementary school from the west area of Santa Maria city. Difficulties presented by them were concentrated primarily in the use of algorithms of the four operations and more particularly in the division operation. They had interpretive skills, but they had many difficulties to perform the calculations due to flaws on the field and understanding of mathematical operations that are fundamental to the continuation of any learning in this science. The participants in this study showed that gaps in teaching and learning needed and must be overcome to continue developing satisfactorily educational future steps. Technological resources are great tools that assist in the construction of knowledge, but they need a good base generated in the classroom promoted by teaching processes. At the end of this research it was possible to observe a great improvement on the use of technological resources (computer, internet, data show, hypertext and treasure hunt) the interpretation and analysis of problem situations, more safety, consistency and understanding in resolving four mathematical operations and their correct use. / Esta pesquisa teve como objetivo verificar as contribuições da construção da aula, em interação com o uso dos recursos midiáticos para potencializar o desenvolvimento de habilidades e minimizar as lacunas do conhecimento matemático nos anos finais do Ensino Fundamental. Na tentativa de superação destas lacunas, a pesquisa ocorreu em dois momentos distintos de aplicação de propostas de atividades: o primeiro foi a aula e seu processo de ensinagem, servindo de suporte e preparação para o segundo momento, que contou com as atividades interativas por meio da Caça ao Tesouro, usando como recurso tecnológico o computador e suas interfaces para melhor qualificar a aprendizagem colaborativa. A investigação foi realizada com estudantes do 6º ano do Ensino Fundamental de uma escola pública municipal, no município de Santa Maria, RS, na região oeste desta cidade. As dificuldades por eles apresentadas estavam concentradas basicamente no uso dos algoritmos das quatro operações e mais especificamente na operação divisão. Eles tinham habilidades interpretativas, mas apresentavam muitas dificuldades para executarem os cálculos devido às lacunas existentes quanto ao domínio e entendimento das operações matemáticas, que são fundamentais para a continuidade de qualquer aprendizagem nesta ciência. Os participantes desta pesquisa mostraram que as lacunas de ensino e aprendizagem precisavam e deviam ser superadas para continuarem desenvolvendo satisfatoriamente as etapas educacionais futuras. Os recursos tecnológicos são ferramentas que auxiliam na construção do conhecimento, mas que precisam de uma boa base gerada na sala de aula promovida pelos processos de ensinagens. Ao final desta pesquisa foi possível observar um grande progresso em relação à utilização dos recursos tecnológicos ( computador, internet, data show, hipertextos e caça ao tesouro) à interpretação e análise de dados das situações problemas, mais segurança, coerência e entendimento na resolução das quatro operações matemáticas e o seu uso correto.

The use of tablets in preschool has increased during the last years. Not everyone is positiveabout young children in preschool, using a technological tool already in at such an early age. Inthis bachelor thesis within the science area of informatics, the researchers research about whateffects the use of tablets in preschool has on children's mathematical knowledge.The result shows the effects on children's mathematical knowledge when using tablets inpreschool. The effects may depend on how the tablet is used in education and also if the use ofthe tablet is guided or not by a preschool teacher. How the tablets are used appears different invarious departments. Some departments in preschool use the tablet more and others less.Preschool teachers want to develop the use of tablets since they see the tablets as an educationaltool.

In the past two decades there has been an increased effort to understand the depth to which mathematics teachers must know their subject to teach it effectively. Researchers have termed this type of knowledge mathematical knowledge for teaching (MKT). Even though recent studies have focused on MKT, the current literature on the subject indicates that this area remains underdeveloped. In an attempt to further refine our conception of MKT this study looked at MKT in Japan. In this thesis I explored and categorized the MKT of three experienced Japanese cooperating teachers (CTs) by looking at the content of their conversations with three Japanese student teachers (STs). I separated the MKT mentioned in these conversations into three categories: knowledge about the students' mathematical knowledge, knowledge about mathematics, and knowledge about school mathematics. I also discussed various implications of this work on the field of MKT.

Syftet med denna studie är att undersöka hur lärare upptäcker elever i behov av särskilt stöd inom matematikundervisningen. Fyra intervjuer har genomförts med två klasslärare respektive två speciallärare, från tre olika skolor. Resultatet indikerar att lärare huvudsakligen upptäcker elever i behov av särskilt stöd genom att se till elever med hög frånvaro och genom diskussion med andra lärare. Gemensamt för alla respondenter är att de påpekar att det är elever som når låga resultat i tester under en längre period som är i behov av det särskilda stödet. Resultatet diskuteras i förhållande till ett ramverk som beskriver lärarkunskaper för matematiklärare. Slutsatsen som dras är att kunskapen att upptäcka elever i behov av särskilt stöd är en viktig lärarkunskap.

South African learners underachieve in mathematics. The many different factors that influence this underachievement include mathematics teachers' role in teaching mathematics with understanding. The question arises as to how teachers' mathematical content knowledge states can be transformed to positively impact learners' achievement in mathematics. In this study, different kinds of teachers' knowledge needed for teaching mathematics were discussed against the background of research in this area, which included the work of Shulman, Ma and Ball. From this study an important kind of knowledge, namely mathematical content knowledge for teaching (MCKfT), was identified and a teacher's ability to unpack mathematical knowledge and understanding was highlighted as a vital characteristic of MCKfT. To determine further characteristics of MCKfT, the study focussed on the nature of mathematics, different kinds of mathematical content knowledge (procedural and conceptual), cognitive processes (problem solving, reasoning, communication, connections and representations) involved in doing mathematics and the development of mathematical understanding (instrumental vs. relational understanding). The influence of understanding different problem contexts and teachers' ability to develop reflective practices in teaching and learning mathematics were discussed and connected to a teacher's ability to unpack mathematical knowledge and understanding. In this regard, the role of teachers' prior knowledge or current mathematical content knowledge states was discussed extensively. These theoretical investigations led to identifying the characteristics of MCKfT, which in turn resulted in theoretical criteria for the development of MCKfT. The theoretical study provided criteria with which teachers' current mathematical content knowledge states could be analysed. This prompted the development of a diagnostic instrument consisting of questions on proportional reasoning and functions. A qualitative study was undertaken in the form of a diagnostic content analysis on teachers' current mathematical content knowledge states. A group of secondary school mathematics teachers (N=128) involved in the Sediba Project formed the study population. The Sediba Project is an in-service teacher training program for mathematics teachers over a period of two years. These teachers were divided into three sub-groups according to the number of years they had been involved in the Sediba Project at that stage. The teachers' current mathematical content knowledge states were analysed with respect to the theoretically determined characteristics of and criteria for the development of MCKfT. These criteria led to a theoretical framework for assessing teachers' current mathematical content knowledge states. The first four attributes consisted of the steps involved in mathematical problem solving skills, namely conceptual knowledge (which implies a deep understanding of the problem), procedural knowledge (which is reflected in the correct choice of a procedure), the ability to correctly execute the procedure and the insight to give a valid interpretation of the answer. Attribute five constituted the completion of these four attributes. The final six attributes were an understanding of different representations, communication of understanding in writing, reasoning skills, recognition of connections among different mathematical ideas, the ability to unpack mathematical understanding and understanding the context a problem is set in. Quantitative analyses were done on the obtained results for the diagnostic content analysis to determine the reliability of the constructed diagnostic instrument and to search for statistically significant differences among the responses of the different sub-groups. Results seemed to indicate that those teachers involved in the Sediba Project for one or two years had benefited from the in-service teacher training program. However, the impact of this teachers' training program was clearly influenced by the teachers' prior knowledge of mathematics. It became clear that conceptual understanding of foundation, intermediate and senior phase school mathematics that should form a sound mathematical knowledge base for more advanced topics in the school curriculum, is for the most part procedurally based with little or no conceptual understanding. The conclusion was that these teachers' current mathematical content knowledge states did not correspond to the characteristics of MCKfT and therefore displayed a need for the development of teachers' current mathematical content knowledge states according to the proposed criteria and model for the development of MCKfT. The recommendations were based on the fact that the training that these teachers had been receiving with respect to the development of MCKfT is inadequate to prepare them to teach mathematics with understanding. Teachers' prior knowledge should be exposed so that training can focus on the transformation of current mathematical content knowledge states according to the characteristics of MCKfT. A model for the development of MCKfT was proposed. The innermost idea behind this model is that a habit of reflective practices should be developed with respect to the characteristics of MCKfT to enable a mathematics teacher to communicate and unpack mathematical knowledge and understanding and consequently solve mathematical problems and teach mathematics with understanding. Key words for indexing: school mathematics, teacher knowledge, mathematical content knowledge, mathematical content knowledge for teaching, mathematical knowledge acquisition, mathematics teacher education / Thesis (Ph.D. (Education))--North-West University, Potchefstroom Campus, 2007.

Submitted by Kenia Bernini (kenia.bernini@ufpel.edu.br) on 2018-02-28T20:32:17Z No. of bitstreams: 3 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Ivan_Britto_Barreto_Dissertação.pdf: 891006 bytes, checksum: e0cd60550acb96d3ad1a85d5593ee0f6 (MD5) Ivan_Britto_Barreto_Produto.pdf: 941244 bytes, checksum: ee8d7dbec8e66f0df368c160e9044019 (MD5) / Approved for entry into archive by Aline Batista (alinehb.ufpel@gmail.com) on 2018-03-05T21:12:13Z (GMT) No. of bitstreams: 3 Ivan_Britto_Barreto_Dissertação.pdf: 891006 bytes, checksum: e0cd60550acb96d3ad1a85d5593ee0f6 (MD5) Ivan_Britto_Barreto_Produto.pdf: 941244 bytes, checksum: ee8d7dbec8e66f0df368c160e9044019 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Aline Batista (alinehb.ufpel@gmail.com) on 2018-03-05T21:12:19Z (GMT) No. of bitstreams: 3 Ivan_Britto_Barreto_Dissertação.pdf: 891006 bytes, checksum: e0cd60550acb96d3ad1a85d5593ee0f6 (MD5) Ivan_Britto_Barreto_Produto.pdf: 941244 bytes, checksum: ee8d7dbec8e66f0df368c160e9044019 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-03-05T21:12:26Z (GMT). No. of bitstreams: 3 Ivan_Britto_Barreto_Dissertação.pdf: 891006 bytes, checksum: e0cd60550acb96d3ad1a85d5593ee0f6 (MD5) Ivan_Britto_Barreto_Produto.pdf: 941244 bytes, checksum: ee8d7dbec8e66f0df368c160e9044019 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-04-03 / A escolha do tema História de Vida, é um objetivo de estudo, pela sua relevância, pois a preocupação de não se deixar passar a importância da trajetória dos professores de Matemática. Assim, esta dissertação possui por objetivo de trazer a história de vida do professor Lino de Jesus Soares um dos professores de Matemática mais conhecidos em nossa região, e pelos seus quase setenta anos que permaneceu em sala de aula. A pesquisa tem abordagem qualitativa, sendo realizada através de entrevista narrativa, com perguntas disparadoras, conforme os estudos de Moreira (2004). Nos relatos das entrevistas realizadas com o professor Lino, foi possível perceber importância do conhecimento de Matemática que é ensinado e o papel fundamental que a História da Matemática possui no processo de ensino. Essa pesquisa se tornará um livro, que ao ser publicado permitirá a toda comunidade ter o registro de vida desse grande mestre / The choice of the theme History of Life, is a study objective, because of its relevance, because the concern is not to overlook the importance of the trajectory of mathematics teachers. Thus, this dissertation aims to bring the life story of Professor Lino de Jesus Soares one of the best-known mathematics teachers in our region, and for his nearly seventy years he remained in the classroom. The research has a qualitative approach, being carried out through a narrative interview, with triggering questions, according to the studies of Moreira (2004). In the reports of the interviews with Professor Lino, it was possible to understand the importance of the knowledge of Mathematics that is taught and the fundamental role that the History of Mathematics has in the teaching process. This research will become a book, which when published will allow the entire community to have the record of this great master's life

In the past decade, mathematics performance by all students, especially minority students in low socioeconomic schools, has shown limited improvement nationwide (NCES, 2011). Traditionally in the United States, mathematics has consisted of arithmetic and computational fluency; however, mathematics researchers widely believe that this method of instruction does not enhance the development of mathematical reasoning and ignores the research on students’ mathematical development (Blanton & Kaput, 2005; Stigler & Hiebert, 1999). Recommendations by the mathematics community are to broaden and strengthen teacher content knowledge in mathematics and to provide the pedagogical tools needed by teachers to extend their students’ thinking and reasoning (Darling-Hammond, Wei, Andree, Richardson, and Orphanos, 2009; Mewborn, 2003). The purpose of this quantitative study was to investigate the relationship between the teachers’ levels of noticing, the levels of cognitive demand in their enacted tasks, and their levels of mathematical knowledge for teaching in two urban high-need low performing elementary schools. The 54 elementary teachers participated in a long-term mathematics professional development program aimed at developing teachers’ mathematical knowledge for teaching and recognizing and fostering students’ early algebraic reasoning. The data for this dissertation included teachers’ self-selected video segments, written video reflections, and mathematical knowledge for teaching levels from the second year of the professional development. Relationships were explored between mathematical knowledge for teaching, teachers’ levels of noticing, and the levels of cognitive demand represented in mathematics lessons. The findings indicated shifts in teachers’ cognitive demand of enacted tasks and noticing over the course of the second year of professional development. Correlation results indicated significant relationships between teachers’ cognitive demand, teacher noticing, participation, and teachers’ mathematical knowledge for teaching. Moreover, the results showed that the teachers in the K-3 cohort benefited more from the professional development than their 4-6 cohort counterparts when it came to mathematical knowledge for teaching, noticing, and cognitive demand levels.

South African learners underachieve in mathematics. The many different factors that influence this underachievement include mathematics teachers' role in teaching mathematics with understanding. The question arises as to how teachers' mathematical content knowledge states can be transformed to positively impact learners' achievement in mathematics. In this study, different kinds of teachers' knowledge needed for teaching mathematics were discussed against the background of research in this area, which included the work of Shulman, Ma and Ball. From this study an important kind of knowledge, namely mathematical content knowledge for teaching (MCKfT), was identified and a teacher's ability to unpack mathematical knowledge and understanding was highlighted as a vital characteristic of MCKfT. To determine further characteristics of MCKfT, the study focussed on the nature of mathematics, different kinds of mathematical content knowledge (procedural and conceptual), cognitive processes (problem solving, reasoning, communication, connections and representations) involved in doing mathematics and the development of mathematical understanding (instrumental vs. relational understanding). The influence of understanding different problem contexts and teachers' ability to develop reflective practices in teaching and learning mathematics were discussed and connected to a teacher's ability to unpack mathematical knowledge and understanding. In this regard, the role of teachers' prior knowledge or current mathematical content knowledge states was discussed extensively. These theoretical investigations led to identifying the characteristics of MCKfT, which in turn resulted in theoretical criteria for the development of MCKfT. The theoretical study provided criteria with which teachers' current mathematical content knowledge states could be analysed. This prompted the development of a diagnostic instrument consisting of questions on proportional reasoning and functions. A qualitative study was undertaken in the form of a diagnostic content analysis on teachers' current mathematical content knowledge states. A group of secondary school mathematics teachers (N=128) involved in the Sediba Project formed the study population. The Sediba Project is an in-service teacher training program for mathematics teachers over a period of two years. These teachers were divided into three sub-groups according to the number of years they had been involved in the Sediba Project at that stage. The teachers' current mathematical content knowledge states were analysed with respect to the theoretically determined characteristics of and criteria for the development of MCKfT. These criteria led to a theoretical framework for assessing teachers' current mathematical content knowledge states. The first four attributes consisted of the steps involved in mathematical problem solving skills, namely conceptual knowledge (which implies a deep understanding of the problem), procedural knowledge (which is reflected in the correct choice of a procedure), the ability to correctly execute the procedure and the insight to give a valid interpretation of the answer. Attribute five constituted the completion of these four attributes. The final six attributes were an understanding of different representations, communication of understanding in writing, reasoning skills, recognition of connections among different mathematical ideas, the ability to unpack mathematical understanding and understanding the context a problem is set in. Quantitative analyses were done on the obtained results for the diagnostic content analysis to determine the reliability of the constructed diagnostic instrument and to search for statistically significant differences among the responses of the different sub-groups. Results seemed to indicate that those teachers involved in the Sediba Project for one or two years had benefited from the in-service teacher training program. However, the impact of this teachers' training program was clearly influenced by the teachers' prior knowledge of mathematics. It became clear that conceptual understanding of foundation, intermediate and senior phase school mathematics that should form a sound mathematical knowledge base for more advanced topics in the school curriculum, is for the most part procedurally based with little or no conceptual understanding. The conclusion was that these teachers' current mathematical content knowledge states did not correspond to the characteristics of MCKfT and therefore displayed a need for the development of teachers' current mathematical content knowledge states according to the proposed criteria and model for the development of MCKfT. The recommendations were based on the fact that the training that these teachers had been receiving with respect to the development of MCKfT is inadequate to prepare them to teach mathematics with understanding. Teachers' prior knowledge should be exposed so that training can focus on the transformation of current mathematical content knowledge states according to the characteristics of MCKfT. A model for the development of MCKfT was proposed. The innermost idea behind this model is that a habit of reflective practices should be developed with respect to the characteristics of MCKfT to enable a mathematics teacher to communicate and unpack mathematical knowledge and understanding and consequently solve mathematical problems and teach mathematics with understanding. Key words for indexing: school mathematics, teacher knowledge, mathematical content knowledge, mathematical content knowledge for teaching, mathematical knowledge acquisition, mathematics teacher education / Thesis (Ph.D. (Education))--North-West University, Potchefstroom Campus, 2007.

abstract: This study contributes to the ongoing discussion of Mathematical Knowledge for Teaching (MKT). It investigates the case of Rico, a high school mathematics teacher who had become known to his colleagues and his students as a superbly effective mathematics teacher. His students not only developed excellent mathematical skills, they also developed deep understanding of the mathematics they learned. Moreover, Rico redesigned his curricula and instruction completely so that they provided a means of support for his students to learn mathematics the way he intended. The purpose of this study was to understand the sources of Rico's effectiveness. The data for this study was generated in three phases. Phase I included videos of Rico's lessons during one semester of an Algebra II course, post-lesson reflections, and Rico's self-constructed instructional materials. An analysis of Phase I data led to Phase II, which consisted of eight extensive stimulated-reflection interviews with Rico. Phase III consisted of a conceptual analysis of the prior phases with the aim of creating models of Rico's mathematical conceptions, his conceptions of his students' mathematical understandings, and his images of instruction and instructional design. Findings revealed that Rico had developed profound personal understandings, grounded in quantitative reasoning, of the mathematics that he taught, and profound pedagogical understandings that supported these very same ways of thinking in his students. Rico's redesign was driven by three factors: (1) the particular way in which Rico himself understood the mathematics he taught, (2) his reflective awareness of those ways of thinking, and (3) his ability to envision what students might learn from different instructional approaches. Rico always considered what someone might already need to understand in order to understand "this" in the way he was thinking of it, and how understanding "this" might help students understand related ideas or methods. Rico's continual reflection on the mathematics he knew so as to make it more coherent, and his continual orientation to imagining how these meanings might work for students' learning, made Rico's mathematics become a mathematics of students--impacting how he assessed his practice and engaging him in a continual process of developing MKT. / Dissertation/Thesis / Ph.D. Mathematics 2011

abstract: A teacher’s mathematical knowledge for teaching impacts the teacher’s pedagogical actions and goals (Marfai & Carlson, 2012; Moore, Teuscher, & Carlson, 2011), and a teacher’s instructional goals (Webb, 2011) influences the development of the teacher’s content knowledge for teaching. This study aimed to characterize the reciprocal relationship between a teacher’s mathematical knowledge for teaching and pedagogical goals. Two exploratory studies produced a framework to characterize a teacher’s mathematical goals for student learning. A case study was then conducted to investigate the effect of a professional developmental intervention designed to impact a teacher’s mathematical goals. The guiding research questions for this study were: (a) what is the effect of a professional development intervention, designed to perturb a teacher’s pedagogical goals for student learning to be more attentive to students’ thinking and learning, on a teacher’s views of teaching, stated goals for student learning, and overarching goals for students’ success in mathematics, and (b) what role does a teacher's mathematical teaching orientation and mathematical knowledge for teaching have on a teacher’s stated and overarching goals for student learning? Analysis of the data from this investigation revealed that a conceptual curriculum supported the advancement of a teacher’s thinking regarding the key ideas of mathematics of lessons, but without time to reflect and plan, the teacher made limited connections between the key mathematical ideas within and across lessons. The teacher’s overarching goals for supporting student learning and views of teaching mathematics also had a significant influence on her curricular choices and pedagogical moves when teaching. The findings further revealed that a teacher’s limited meanings for proportionality contributed to the teacher struggling during teaching to support students’ learning of concepts that relied on understanding proportionality. After experiencing this struggle the teacher reverted back to using skill-based lessons she had used before. The findings suggest a need for further research on the impact of professional development of teachers, both in building meanings of key mathematical ideas of a teacher’s lessons, and in professional support and time for teachers to build stronger mathematical meanings, reflect on student thinking and learning, and reconsider one’s instructional goals. / Dissertation/Thesis / Doctoral Dissertation Mathematics Education 2016